Atomic Energy of Canada Limited

THORIUM DIFFUSION IN THQRIA AND URANIA

by

A.D. KING

Chalk River, Ontario

August 1970

. „ AECL-3655

THORIUM DIFFUSION IN THORIA AND URANIA

A.D. King

Materials Science BranchChalk River Nuclear Laboratories

CHALK RIVER, Ontario, Canada

ABSTRACT

Techniques are described for the measurement ofdiffusion in ThO2 and U02« Results are presented for singlecrystal ThO2 in the range 1850 to 2000°C and single crystal UO2at 1575°c. The diffusion profiles are interpreted in terms oflattice and dislocation diffusion coefficients. Previous dataon cation diffusion in ThO2 and UO2 are discussed.

August, 1970

AECL-3655

Diffusion du thorium dans le thoria et l'urania

par A.D. King

Section de s-ciences des matériaux

Résumé

Des techniques sont décrites pour la mesure de la

diffusion de "°Th dans ThO2 et U02- Les résultats sont

présentés pour de simples cristaux de ThO2 dans la gamine

allant de 1850 a 2000°C et pour de simples cristaux de

U02 a 1575°C. Les profils de diffusion sont interprétés

en fonction des coefficients de diffusion de dislocation et

de réseau. Des données antérieures concernant la diffusion

de cations dans le ThO2 et l'U02 font l'objet de commentaires.

L'Energie Atomique du Canada, Limitée

Laboratoires nucléaires de Chalk. River

Chalk River, Ontario

Juillet 1970

AECL-3655

THORIUM DIFFUSION IN THORIA AND URANIA

A. D. King

Materials Science BranchChalk River Nuclear Laboratories

CHALK RIVER, Ontario, Canada

1. INTRODUCTION

In recent years there has been a growing number ofstudies of diffusion in the nuclear ceramic oxides U02» TI1O2and some mixed oxide systems. Most of this work has beenconcerned with uranium dioxide (see the review by Belle,ref. 1) but quite recently several investigations of diffu-sion in thoria have been undertaken(2-5). Both UO2 andThO2 are oxides of the fluorite type for which diffusion inthe cation sublattice is many orders of magnitude slower thanoxygen diffusion, and is thought to be of fundamental impor-tance in many high temperature processes which depend on masstransport.

As a result of the small cation-diffusion coeffic-ients the isotope penetration, in a tracer-isotope self-diffusion experiment, is restricted, and somewhat specializedtechniques are needed for diffusion measurements. This re-port describes techniques which have been developed at ChalkRiver for the measurement of thorium ion diffusion in ThO2(primarily) and U02»

2. CHOICE OF TECHNIQUE

There are essentially three techniques which couldbe used: viz. the "surface activity decrease" method, alphaspectrometry, and sectioning. All three techniques have beenemployed for the measurement of uranium diffusion in UO2 (seeTable 2, ref. 1).

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The first two are particularly sui ted to the measure-ment of small diffusion coefficients. When lattice diffusionis very slow, however, faster diffusion processes such asoccur via grain boundaries or dislocations are important. The"surface activity decrease" method would then be unsuitableas the presence of any faster diffusion process would lead toan over-estimate of the lattice diffusion coefficient. Thismethod may also be in error due to evaporation of the tracerfrom the surface.

The a-spectrometry technique may also be of limitedusefulness. This method uses the fact that characteristica"s emitted by the tracer isotope, which reach the surfacefrom the depth to which the isotope has diffused, will havelost some of their energy. The isotope concentration profilecan thus be determined from the a spectrum at the surface.Although the range of a1 s from thorium isotop«>s may be ^10pmor so, in practice the count rates of lower energy a particlesemerging from depths greater than about 2|jm are usually neg-ligible with respect to the background. Thus, the restrictedrange of diffusion distances which can be observed with thismethod is a limitation, especially if more than one diffusionmechanism is operative.

Sectioning is the most direct method for determininga diffusion profile but most sectioning techniques are toocrude for the determination of very small diffusion distances(2/Dt say ~l|jm). Further, the commonly used weight-loss methodfor measuring section thickness is not suitable for sectionsof thickness less than about 2pm. However, if a suitablemethod exists for measuring the small amounts of specimen re-moved, the sectioning technique can be extended to the deter-mination of very small diffusion coefficients(6).

A rough estimate of the section thicknesses (and thedegree of surface flatness and perfection) required in ourcase may be deduced from previous work. For both ThO2 and"stoichiometric" UO2 a reasonable value for the diffusioncoefficient at say ̂ 0.6 T m (a relatively easily attainabletemperature even for thoria) might be 10-14 cm2/sec. For a48 hour diffusion anneal, therefore, 2/Dt would be of the

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order of lpm. Thus, the near-surface sections should be notmore than O.lum thick and the specimen surface should besubstantially free of surface irregularities of depth greaterthan ^0.01pm.

In the present work a sectioning technique whichsatisfies these requirements has been developed. The thoriasection thicknesses can be determined by neutron activationanalysis: for KO2 the 1-(2-Pyridylazo)-2 Napthal method ofuranium analysis has been used.

Some a-spectrometry measurements have also been madeand are found to give results in good agreement with thesectioning data.

3. SPECIMEN MATERIAL

Specimens of area ~0.5 cm^ and 0.1 cm thickness werecut with a diamond wheel from arc-fused lumps supplied bythe Norton Co. Some analyses of these materials are shownin Table 1. Rather wide variations between samples have beenobserved..

As supplied, the thoria lumps were usually dark redor blackish but sometimes were brown or pink; the semi trans-parent slices being mainly light bxown or bluish grey.

The as-received UO2 contained metallic uranium andsubstantial amounts of carbon and nitrogen. A reduction inthe carbon and nitrogen content, and approximate stoichiometry,was achieved by a heat treatment, together with green UO2pellets, to 1500°C in flowing hydrogen.

4. TRACER ISOTOPE

The ^^Th tracer was evaporated as oxide using anelectron beam gun. Prior to the evaporation the daughter pro-ducts 212pb, 224Ra and 208pb were removed, for reasons givenin section 6.3, by precipitation as sulphate (v/ith BaSO4carrier) from aqueous solution of the nitrate. The electron

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gun was also used for discharge cleaning of the specimens.The specimens were shielded until the ThO2 isotope sourcewas melted so that any remaining impurities would be vola-tilized before the evaporation.

The film thickness was generally ~500 to 1000Â (asestablished by neutron activation analysis of natural thoriadeposited on pieces of magnesium oxide during similar eva-poration) .

5. ANNEALING

Two furnaces were used for the diffusion anneals andpre-anneals. One was a horizontal tantalum tube resistancefurnace equipped with tantalum heat shields; the other avertical furnace which had a split tungsten mesh heating ele-ment and tungsten and molybdenum heat shields.

All anneals to date have been performed under astatic argon atmosphere of a few psi above atmosphe.vic pres-sure, to reduce evaporation from the specimens. The natureof the heating elements is then of importance. The oxygenpartial pressure established in the "tantalum" furnace wasexpected on thermodynamic grounds to be much lower than inthe "tungsten" furnace. In fact, thoria crystals annealedin the tantalum furnace at ̂ 1800°c turned grey or black,possibly indicating that reduction was occurring, whereasin the tungsten furnace they remained basically transparenton heating to at least ̂ 2200°C.

Specimens were wrapped in clean tantalum or molybdenumfoil, and contained in thoria crucibles on which the opticalpyrometer was sighted. Temperatures were measured using twoL and N optical pyrometers, one of which was calibrated againsta standard lamp at the National Research Council. The tempera-ture was maintained constant in the vertical furnace withinthe limits of error of the pyrometer reading (5°C) and constantwithin ±10°C in the horizontal furnace. Corrections dua totha furnace sight glass, and the right angle prism used withthe horizontal furnace, were determined.

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Emissivity corrections were obtained by measuringthe effective emissivity of sintered thoria in the twofurnaces. In the tungsten furnace in which readings weretaken through a split in the heating element, the effectiveemissivity was unity. In the tantalum furnace an effectiveemissivity of 0.59 ±0.1 was obtained and used to correctthe observed temperatures. Results were rather scattered andthe possible error allows an appreciable error (iv-25°C at^1900°C) in the quoted temperatures.

6. SECTIONING TECHNIQUE

6.1 Surface Preparation

The initial surface preparation and post-annealsectioning were both performed using the automatic polish-ing machine described below. The refinement of these pro-cedures was crucial for the successful application of thesectioning technique.

To prepare the surface a variety of lapping techniqueswas tried. The procedure finally adopted was first to grindthe specimen flat using diamond paste abrasive on a glassplate, and then to polish it with successively finer gradesof diamond paste on plain paper backed by plate glass. Thisuse of an almost textureless lapping surface gave a highlypolished flat surface.

The polishing machine, is based on that of DeJongheet al(6', and is illustrated in Figure 1. The specimen ismounted on the end of a steel cylinder (C) whose weight U200gm) provides the load for grinding and polishing. Thecylinder slides inside an accurately machined steel collarattached to the reciprocating arm of the machine, and pivotedso that the 4" diameter steel rim (R) of the collar is freeto slide in contact with a 6" diameter plate glass lap.

Electron micrographs of surface replicas showed thatthe polished surfaces were mainly featureless but with a fewfine scratches of width (and depth) ̂ O.aSprn. Scratching wasminimized with machine polishing. Surfaces were optically

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flat except at the edges. Reflection electron diffractionpatterns from the surfaces consisted of rings of diffusescattering typical of a polycrystal or amorphous structure,showing that the surface layer was considerably deformed.Crystallinity was restored by annealing. Some channellingstudies of such annealed specimens confirmed the perfectionof the crystal to within 5̂O.H of the surface.

6.2 Sectioning

Remounting of th^ specimen after the diffusion anneal,so that polishing (sectioning) was continued in the plane ofthe surface, was simply achieved by introducing a 1 mm thicksheet of rubber between the specimen and the end of the steelcylinder. The specimen surface was then automatically orientedto the plane of the lap. Edge rounding was increased but foreach section it was always small compared to the sectionthickness. The specimens were swabbed between each step, andthe swabs «y-counted, so that no particles from the initialactive sections were transferred to the sections at greaterdepths. Less than 1% of the isotope activity removed was re-tained round the specimen, and removed by swabbing, on eachsectioning step.

Vftiatman No. 50 or similar low ash filter papers hada suitable texture for use as the paper laps and did notinterfere with the subsequent analysis for thorium or uranium.

Each section was folded and compressed into a 3/8" dia.by 1/4" polyethylene vial for counting in the scintillationcounter.

6.3 y-Ray Spectrometry

A Y-ray spectrometer was used to determine theactivities in each section, and the subsequent post-irradiationactivities of the thoria sections. A wall type Nal scintilla-tion crystal was used so that the counting rates were not sen-sitive to the geometry of the source.

In the 228iph <y spectrum the most prominant peaks areat ̂ 0.238 meV, due to 212pb decay, and at ̂ .0.08 MeV. The

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latter is mainly an x-ray peak due to the isomeric decay of212ai which effectively masks the relatively weak 0.084 MeVpeak due to 228i>h decay.

In the present work the 228^ concentrations in eachsection were determined by counting the 0.24 MeV 212pb peak.To avoid errors due to diffusion of the daughter productsthemselves, the 2 2 8 ^ isotope was first purified as mentionedin section 4. The sections were counted approximately 2 weeksafter the diffusion anneal, by which time the 212pfc activityhad reached ~95% of its equilibrium value.

6.4 ThO? Section Thickness Determinations

The thorium in each section was determined using thereaction

232Th (n.7> 233Th g^L 233Pa (27.4 d)

The 0.3 MeV 233pa y peak from a near-surface sectionis shown in Figure 2b. (The 212pb COunts from the tracerhave been subtracted; this was not necessary for sections fromgreater depths.) The contribution due to induced backgroundactivity from irradiated impurities was corrected for by de-fining the 233pa counts as indicated in Figure 2b by thehatched area. Allowing for 233pa decay, 233pa counts werethen reproducible within ±1% over a period of time, and wereinsensitive to the amount of background activity.

Counts were normalized with respect to neutron doseby reference to the specific activities of Al/co flux monitorsirradiated with each section, and were compared to similarlynormalized counts from irradiated thorium standards. The237Pa activity/unit weight Th, obtained using a variety ofstandards, was constant to within ̂ ±2% over the range ofinterest (5 to SOOugm Th),

The probable errors in these procedures together withthat in measuring the specimen area give errors ~±5% to ±3%for section thicknesses from £0.05 to ~2pm. The density ofThO2 was taken as 10.0 gm (8K

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6. 5 U0 2 Section Thickness Determinations

The uranium (hence UO2) in each section was deter-mined using the reagent PAN as described by Cheng(9). Thecoloured uranyl dye chelate formed is extracted with o-dichlorbenzene and determined by optical absorption in as pe c tr opho tome ter.

Beer's law was apparently obeyed up to concentrationof ~150|j,gm uranium in 10 ml o-dichlorbenzene (cf ̂ 50(xgmquoted by Cheng). For larger uranium concentrations (typi-cally from sections ;>2|jm thick) 20 or 50 ml of o-dichlor-benzene were used.

This method was less accurate and reliable than theactivation analysis method used for the thoria work. Themain uncertainty was in the recovery of uranium during theanalysis. The apparent recovery of known quantities ofuranium, evaporated from solution onto filter paper and sub-jected to the same separation procedure was generally 100%± 4%. For sections ^O.lpm thick, the accuracy of the sectionthicknesses was probably only ± ?%.

A fluorometric method was tried but was not satis-factory, using the present sectioning techniques, due to sup-pression of fluorescence by some unknown impurity.

7. Ct-SPECTROMETRY

The a-spectra of 228iph an^ its daughter products,before and after diffusion in ThC>2 and UO2 have been measuredusing a lithium-drifted-silicon detector (or for the laterUO2 work a surface-barrier-detector) with associated ampli-fier and multi-channel pulse height analyzer. Some of thespectra are shown in Figure 3. By using the known stoppingpowers (dE/dx) cf TI1O2 or UO2 for a's, a plot of concentrationversus distance can be obtained directly from the a peak shapeafter diffusion, as shown for example in reference 41.

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The simplest peaks to analyze were tha 212po ancj216Po peaks at 8.785 and 6.777 MeV respectively (228Th decayitself gives two closely spaced peaks at 5.34 and 5.42 MeV).Almost immediately after the diffusion anneal the daughterproduct peaks all give essentially a measure of the diffusionof the 3.64 day 224Ra daughter, the other daughters beingrelatively short lived. However, after ~2 weeks when thedaughter products are virtually in equilibium with 228Th,2 2 8Th diffusion may be obtained from analysis of any of thepeaks. In theory the 212Po peak may be used to determinepenetrations up to ~ 8 ^ , the 216po peak for up to ̂ 1. 5pm andthe 6.288 MeV 220Rn and 5.864 MeV 224Ra for the first .-.0.5(jm.In practice the a-count rates from depths greater than ̂ 2pjnhave been very small.

There is some uncertainty in the values of dE/dxused in the calculations. In the present work, calculatedvalues (previously obtained by Schmitz and Lindner (10b) ) havebeen adopted, e.g. for the 216po peak (a energy range ofinterest 6.4 to 6.78 MeV) the theoretical values of dE/dxrange from 254 to 260 keV/|jm for UO2 and from 225 to 230 kev/|jm for ThO2« For computation purposes "mean" values of257 and 228 keV/pm were taken. The theory should be quiteaccurate for a's of these energies(H). The main unknownsare the average excitation energies of the atoms, which areknown for Th, U and oxygen in the oxides, to within a fewpercent(I2).

These values are felt to be more reliable than, forexample, the estimate of 448 kev/pfti for the energy range 1.3to 4.82 MeV adopted by Hawkins and Alcock(2) in their studiesof diffusion in U02-

Other sources of error in the method, due to a varietyof causes, are the finite width and low energy tail of eacha peak, which occur even with an "infinitely thin" source*13'.These limitations of the spectrometer become important whenthe amount of diffusion is small. The effect of the peakwidth can be estimated by assuming the peaks are Gaussian.Por the lithium-drifted-silicon detector used in this work.

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the a peak full width at half maximum (FWHM) was ^30 keV(the surface barrier detector had a FWHM of ~20 keV). FordE/dx «,250 kev/pm this FWHM is therefore equivalent to adistance of 0.12|jm = 2a say. The concentration versus distance profile obtained is then:

(this is a form of the solution derived in ref. 10) where /a= 1.1775/a and M is the total amount of isotope deposited.For /Dt ̂ 0.lum as in most of the present work, and for x ^0.15pm, the right hand bracket in equation (A) is constantwithin~l%and a plot of In c vs x 2 has a slope S of-a/(4aDt+2),i. e.

Dt = « - kThis correction has been applied where necessary. Further-more, the In c vs x 2 plot may be extended to x = 0 by applyingthe factor {l+erf (C x)}~i. This correction was also applied;it was facilitated by the fact that the value of C is rela-tively insensitive to /Dt.

The low energy tail also becomes important when dif-fusion is slight; see f-i. example the thoria runs 3 and 4 inthe results section.

8. RESULTS

The sectioning and a-spectrometry data are analyzedin terms of the diffusion equation solution:

In all cases it was found that plots of log C vs x 2 werenon-linear and the reason for this will be discussed. Forease of discussion, apparent diffusion coefficients wereobtained from the slopes of the plots in different regions ofthe profile.

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8.1 Thorium Diffusion in TI1O2

The diffusion runs were as follows.

i) Two runs (1 and 2) at 1995 ± 35°C in the "tantalum"furnace (i.e. under reducing conditions) for 14 hoursand 50 hours respectively using sectioning. A differ-ent specimen was used for each run. The data are shownin Figures 4 and 5.

Two preliminary sectioning runs, under reducing condi-tions at ̂ 2200 ± 40°C, were performed. Although in-sufficient data points were obtained for an accurateprofile, both also gave non-linear log C vs x2 plots.

ii) in the "tungsten" furnace under essentially non-reducingconditions, run 3 at 1846 ± 10°C for 20 hr using twospecimens (T31 and T32) face to face, and run 4 at 1924± 10°C for 17 hr were made. Log C vs x 2 plots obtainedby both a-spectrometry and sectioning are shown inFigures 6 and 7. Figure 8 shows the data for specimensT31 and T32 plotted as log C vs x.

Two other runs were attempted in this furnace; 15 hrat 2234 ± 10°C and 15 hr at 2129 ± 10°C, but in both casessintering of the specimens to each other and to their surround-ings (the tungsten wire spacers and thoria crucibles) andevaporation of the isotope and extensive evaporation of thespecimens (causing surface faceting) prevented any diffusionprofiles being obtained. It is noteworthy that at similartemperatures in the "tantalum" furnace the amount of evapora-tion and the tendency -o sinter were much reduced.

Considering runs 1 and 2 first, Figure 4 indicatesthe precision obtainable with the sectioning technique, run2 being a particularly good example with 14 sections in thefirst 0.7pm. Both log C vs x 2 plots were apparently linearover about an order of magnitude drop in concentration nearthe surface. However, with increasing x the slopes gradually

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decreased (see Figure 5) and at x ~10|jni the slopes were morethan two orders of magnitude lower than in the near-surfaceregion. An interesting feature which will be discussed isthe apparently low isotope concentrations obtained for x ^0.

In the discussion below it is proposed that the near-surface slopes give the bulk diffusion coefficients. Theseare 4.0 x 10~ 1 5 cm2/sec and 1.9 x 10~ 1 5 cm2/sec for the 14and 50 hr anneals respectively.

The difference could be due to real differences inthe specimens, or to a variation in the diffusion coefficientwith annealing time. There is also the possibility that thetemperature measured for the 1st run was too low due to adeposit of boron nitride evaporated onto the furnace sightglass from a component in the furnace in this run. Otherevidence for this is that a higher furnace current was re-quired in the first run and from the current/temperature re-lation for this furnace it is estimated that the temperatureof the first run could be 50°C higher than measured.

Figure 6 shows the near-surface data from run 3 (nonear-surface sectioning data is shown for T31 as insufficientsections were taken in this case). The data for specimen T32are of particular interest being probably the first detailedcomparison of a-spectrometry and sectioning results. Itappears that as the extent of diffusion was limited, thecounts in the tail of the a-peak due to diffused isotope werenot much above the instrumental background level. For largex approximate corrections (shown in Fig. 3) were estimated,based on the counts in the low energy tails of the a peaksbefore diffusion, giving good agreement with the sectioningdata.

In the rangu 0.2 to 0.6pm the sectioning data forspecimen T32 are apparently consistent (see Figure 6) witha linear log c vs x2 plot over an order of magnitude drop inconcentration giving D = 3.8 x 10~15 cm2/sec. However close

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to the surface the slope is evidently even steeper and asdiscussed below it is perhaps this slope which is most nearlyrepresentative of bulk diffusion.

Considering the a-spectrometry points for x £ 0.2^,the limiting slopes as x - 0 are approximately the same forboth specimens. The near-surface slope 'S' shown in Figure 6for specimen T31 must be corrected by about 30% to give the Dvalue indicated (using the relation 4Dt = 1/s - 2/a given insection 7). Even this value is probably an over-estimate, thelimiting slopes for each specimen giving apparent D's more ofthe order 1-2 x 10~16 cm2/sec.

The sectioning data at greater distances (Figure 8) arenotable for the linear log C vs x plot for specimen T31.

The results for diffusion run 4 (specimen T41) are shownin Figure 7. The sectioning points are in good agreement withthe corrected a-spectrometry data. The degradation of the a-peakwas small which reduces the accuracy of this data. Plot a) inFigure 7 shows the sectioning data within the first 0.2pm indetail. As in runs 1 and 2 there is an initial low point followedby a near-surface region in which the concentration falls by anorder of magnitude, with a slope corresponding to a D of 4.9 x10-16 cm2/sec» The a-data give approximately the same result,after allowing for the correction due to the spectrometer resolu-tion. The slope decreases down to the limit of sectioning at~12pm (not shown in Figure 7). Plot c) in Figure 7 shows howby the right choice of the x 2 scale in the plot, an apparentlylinear region may be obtained in an intermediate range, givinga false value for D.

8. 2 Thorium Diffusion in UO^

Three specimens (Ul to U3) were used for a series ofanneals at ̂ 1570°C in the "tungsten" furnace under a static argonatmosphere. Under these furnace conditions, approximate stoichi-ometry should be maintained (see for example the thermodynamicdata in refs. 14 and 15). In the region of interest, i.e. within~20nm of the surface, the composition appropriate to the anneal-ing conditions should be reached within a few minutes at thisannealing temperature (assuming an oxygen diffusion rate of

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10~8 cm^/sec ̂ ) K It may be noted that even with annealsunder flowing gas mixtures where oxygen content is monitoredbefore and after passing through the furnace, the compositionsof U02 specimens are affected by the type of furnace compon-ent^).

The sequence of experiments was as follows- SpecimensUl and U2 were annealed together, active surfaces facing, for35 hours and 32 hours at 1570 and 1574°C ± 10°C respectively.The a-spectra were examined immediately after each anneal andthen again after 2 weeks when the diffused daughter products hadalmost entirely decayed, and finally sectioned. The specimenswere given a 2 hr anneal at 1400°C after the first sectioningto remove surface deformation. Figures 9 and 10 show thefinal a-spectrometry data and the sectioning data together.The a-spectrometry points shown were obtained by analyzingthe 216po peaks. Analyses of the 212po peaks and the 2 2 0 ^and 224R 9 peaks (for smaller distances) gave identical results.

No "tail" corrections to the a-spectrometry pointswere necessary as diffusion was more extensive than in thethoria runs. The agreement between the sectioning and a-spectrometry results is quite good, although the sectioningpoints were much more scattered than in the thoria work (dueto errors in the section thickness measurements by chemicalanalysis). The profiles are again non-Gaussian.

The 35 hour anneal was interrupted after 4, 7^ and 21hours, and the 32 hour anneal after 14 hours, for examinationof the complete a-spectrum, the daughter products having beenpartially regrown before the anneals for this purpose. Theseintermediate results are of qualitative interest. Basicallythey indicate the combined effects of diffusion of 2 2 8 ^ andthe 3.64 day 22^Ra daughter. The spectra taken immediatelyafter the 35 and 32 hour anneals gave similar results to thosefinally measured, indicating that the 2 2 4Ra diffusion rate issimilar to that of thorium. At each intermediate time theanalyses of the different daughter product peaks all gave es-sentially the same profiles, for each specimen.

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The results show a number of anomalies. First thereare marked differences between the profiles for the twospecimens particularly near the surface. In both runs thelog C vs x 2 curves for specimen U2 actually pass through amaximum near x = 0 (see Figures 9 and 10). In contrast theprofiles for specimen Ul have a very steep slope near theorigin. These features are shown by both the a-spectrometryand sectioning measurements. Secondly, the extent of diffu-sion in both specimens in the second 32 hour anneal is muchless than in the first anneal. in addition, the results atintermediate times indicate greater diffusion rates forshorter annealing times.

The difference between the near-surface profiles ofthe two specimens seems to be because specimen U2, in eachexperiment, initially had the greater amount of tracer acti-vity. Transfer of material through the vapour phase wouldthen lead to anomalously high initial concentrations in speci-men Ul and low initial concentrations in U2. To test this,a third diffusion anneal of 102 hours at 1575 ± 10°C wascarried out using specimens U2, again, and U3. For this ex-periment U2 was given the lesser amount of 2 2 8 ^ tracer.Final analysis was by a-spectrometry. Intermediate analyseswere made after 20, 39 and 59 hours. The profiles are shownin Figure 11. As expected, the profile of specimen U2 nowshows the steep near-surface slope and that of specimen U3 hasa maximum. The depth of specimens affected by these "surface"effects is very large (almost 0.5|jjn after 102 hours annealing).As a result of these effects, apart from the fact that thethin film solution to the diffusion equation should no longerbe strictly valid, it is not possible to obtain a near-surfaceslope for specimen Ul in the first two anneals and U2 in thethird anneal. Slopes are indicated in Figures 9, 10 and 11for specimens U2 and U3 respectively, which are thought togive bulk diffusion coefficients (see the discussion section)although the continuous loss of tracer from the surface mightlower the slopes at greater depths, leading to high D values.The results are given in Table 3.

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9. DISCUSSION

9.1 Present Results

Consider first the reliability of the profiles ob-tained. A basic test of the sectioning technique was madeby performing two control runs (i.e. with no diffusion) oncrystals of TI1O2 and U02- In both cases the "profiles" wereessentially square, as they should be. These results indi-cated the minimum diffusion coefficient which can be measured.For a 30 hr anneal say, this is ̂ 2 x 10-16 cm2/sec. The near-surface sectioning data for the ThO2 runs 3 and 4 are approach-ing this limit.

Other possible sources of error in the sectioning datanear the surface occur in the section thickness determinations.If, as in the UO2 runs in particular, the specimen surfacesare quite heavily pitted due to thermal etching, section thick-nesses, estimated from the amount of specimen removed and thearea, would be too small and lead to anomalously high concen-trations. Alternatively, if during the initial stages ofsectioning edge rounding occurs, low tracer concentrationscould be obtained. The basic agreement between sectioningand a-spectrometry data seems to show that such effects weresmall or balanced out. (See, however, the initial sectioningpoints for specimen Ul in Figure 10.)

It may be mentioned here that the explanation of theanomalously low initial points in the sectioning profiles ofthe ThO2 runs 1, 2 and 4, is the same as that given for thenear-surface anomalies in the UO2 work (see section 8.2);i.e. exchange of surface material between the specimens andthe adjacent natural thoria.

The a-spectrometry data are subject to a number ofpossible errors also (see section 7).

The best argument for the accuracy of the diffusionprofiles and particularly for the typical non-Gaussian shapeis that the sectioning and a-spectrometry results are essen-tially in agreement. The question then is, how can they be

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explained in terms of diffusion mechanisms or other effects?

Non-Gaussian profiles have been observed in a largenumber of systems, both metallic and non-metall.ic. Near-surface anomalies most often occur in studies of impuritydiffusion and explanations put forward in these cases, suchas low solute solubility, should not apply in either of thepresent systems.

High tracer concentrations near x - 0 are oftenattributed to surface hold-up or a surface bound layer (e.g.in studies of UO2 and ThO2, see refs. 2 and 3). This explana-tion certainly applies in such systems as impurity diffusionin aluminum due to surface oxide effects(16). a n analogouseffect seems unlikely for cation diffusion in UO2 and ThC^.In this work rates of sintering and evaporation are relativelyhigh, and affect an appreciable depth of near-surface material,so that it is difficult to see why hold-up, due to poor sur-face contact, for example, should occur. Nevertheless, itmight be noted that Hawkins and Alcock(2) found that carefulcleaning of the specimen surface was necessary before pene-tration of the isotope could take place. However, even withclean surfaces they still observed "anomalously" high concen-trations near x = 0.

A combination of bulk and short circuit diffusion, i.e.via dislocations and subgrain boundaries, could give this typeof effect(17,18). This combination is most likely to occur inexperiments such as the present ones in which measurements ofthe diffusion of a very slow moving species were attempted atrelatively low temperature U-0.6

Harrison (1^) has given a general classification ofthe kinetics of dislocation enhanced diffusion, in which hedistinguishes between types "A" and "C" diffusion as limitingcases in which Fick's law behaviour would be observed. TypeA behaviour occurs when the scale of the dislocation networkis small compared to the diffusion distance so that diffusiontakes place primarily through the network but also into theintervening regions. If most of the dislocations are concen-trated in the boundaries of subgrains (grain size = ag) the

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most restrictive condition for type A diffusion iaq « yDgt, where Dg is the lattice diffusion coefficient.More realistically, the condition is that ag « /Dct whereDc is the diffusion coefficient for all atoms in the system,obtained from a sectioning experiment. Dc is related to Dg

and D<j, the diffusion coefficient in the short circuitingpaths, by:

Dc = f Dd + (1-f) Dg

where f is the fraction of the specimen volume located in theregions of enhanced diffusivity.

Type C diffusion occurs when diffusion proceeds en-tirely via dislocations; the condition is: /Dgt « 6 where6 is the width of the region of high diffusivity. Usually6 is too small for this situation to be observable. However,for ionic crystals there is growing evidence that the regionsof enhanced extrinsic diffusivity (due to impurity segrega-tion) may be very extensive and 6 may be of the order ofmicrons (see for example ref. 20). The diffusion coefficientobtained from a sectioning experiment is just D^.

In general there will be a transition from type C totype A diffusion as t increases from very short to very longtimes. When the limiting conditions are not met, Harrison'stype B diffusion occurs and Fick's law is not obeyed. Thisseems to be the case in the present work and in most studiesin which the diffusion profile is examined in sufficient de-tail (18).

The theory of grain boundary diffusion has been treatedby a number of authors, notably Fisher (2D (a much simplifiedtreatment) and Whipple^22) (the most complete treatment). Thevarious treatments have been reviewed and compared by LeClaireThe boundary is treated as a slab, of width 6, of high diffusi-vity material. The tracer concentration at the free surfaceis assumed to be constant (which is not normally the case) inmost theories but Suzuoka(24) has considered the case of a thinfinite layer of diffusing material (but with no diffusion para-llel to the surface within the layer, which is also not normally

- 19 -

realistic). However, it appears that the value of the grainboundary diffusion coefficient obtained from a sectioningexperiment is fairly insensitive to the type of solution(23).Similar treatments of dislocations (treated as cylindricalpipes) and subgrain boundaries (treated as assemblies of dis-location pipes) have been made (25~27)_

All these theories of type B diffusion give theapproximate result that for deeper penetrations beyond theregion in which direct bulk diffusion occurs, the tracerconcentration falls exponentially with distance rather thanwith distance squared. As x - 0 the diffusion profile tendsto that for bulk diffusion, i.e. log C a x .

The present diffusion profiles are approximately ofthis type, specimens Tl and T31 being particularly good ex-amples.

It is of interest to consider the dislocation struc-tures of the specimens used. Some divergent beam x-ray pat-terns have been taken of the thoria specimens T31, T32 andT4 by G. R. Goldak at the University of Saskatchewan, (aftera two hour anneal at 1800°C to remove surface deformationcaused by sectioning). The patterns indicated a high degreeof crystal perfection with little substructure and a low dis-location content (say <105 dislocations/cm^). However, thermaletch pitting of these specimens revealed a distinct subgrainstructure. The average diameter of the subgrains was ,^0.04 cm.Assuming for argument's sake that each subgrain is made up ofedge dislocations of Burgers vector ~5A, separation L, and amisorientation between the subgrains of ̂ 0.1° (as found for anumber of UO?, single crystals (28) ), we have:

s i n

and the number of dislocations/cm2, counting only those in thestabyrain boundaries, is:

— — x — 2 x 10 dislocations/cm .~ 0.04 L

It is evident that the scale of the short circuiting paths ismuch too large for a type A situation to exist. (However, it

- 20 -

is also of interest that type A diffusion has been observedin systems in which the observed dislocation densities areapparently too small to satisfy Harrison's criteria, see forexample reference 29 .

Ths UO2 crystals have not been examined by x-raytechniques and do not show the same type of thermal etchpitting as the thoria specimens. However, the dislocationcontents of similar arc-fused UO2 crystals have recentlybeen thoroughly investigated by Chapman et al ' '. The dis-location densities were ~107/cm2. Type B diffusion shouldagain have been observed although with the greater diffusionrates in the UO2 specimens the conditions were presumablycloser to type A diffusion than in the thoria work. A pos-sible complicating factor is that for specimens preparedwith cut and polished surfaces, the dislocation density, evenafter prolonged annealing, may be a function of distance fromthe polished surface (e.g. ref. 30).

Considering now the thoria data, for which type Bdiffusion seems to apply, quantitative analysis of the shortcircuiting diffusion is possible. If the dislocations aremostly located in the subgrain boundaries of width 6 =- a2/L,say, where a is the dislocation "pipe" diameter and L thedistance between dislocations in the boundary, then for largex, using the simple Fisher type treatment:

_iwhere A has the value rr (see ref. 23 for a discussion ofthis "constant").

Now if the amount of diffusion down the high diffusi-vity paths were small, the majority of the profile would berepresentative of bulk diffusion and log C vs x 2 would belinear over say at least two orders of magnitude in concentra-tion near the surface. In the present work the range of near-surface linearity is never more than one order of magnitudeand the amount of tracer isotope in the tail region, i.e. be-yond the initial "linear" region, is large. The profiles ofspecimens Tl and T2 for example have respectively ~25% and

- 21 -

6% of the tracer in the tail*. Thus, although the near-surface slopes of the log C vs x 2 plots should be most nearlyrepresentative of the bulk diffusion, they are probably in-fluenced by dislocation diffusion, and the resulting Dy valuesare upper limits for the true volume diffusion coefficients.

Taule 2 shows the values of Dy for Th in ThO2 obtainedfrom the near-surface slopes, and va1aes of D^B obtained fromequation (1) using these values of Dy and the limiting valuesof 9 In c/9 x at large x.

The UO2 measurements were generally not sufficient atgreater penetrations for similar calculations to be possible.However, in the first run specimen Ul was sectioned to ̂ 6|jm,and log C was found to be linear in x2 rather than x in thetail region.

The UO2 near-surface results given in Table 3 may alsobe considered in the light of dislocation effects. The appar-ent diffusion coefficients for specimens U2 and U3 in the 2ndand 3rd runs decreased with time towards a limiting value of-1.5 x 10~15 cm2/sec. The value 1 x 10"^ cm2/sec determinedfor U2 after the first (35 hr) anneal is basically due to afast initial diffusion rate. Thereafter, the diffusion rateas measured by the change in profiles between intermediateanneals was much smaller. The time dependence may be connectedwith the fact that these diffusion coefficients are probablyenhanced by a contribution from dislocation diffusion (seepage 24).

A similar time dependence has been observed for UO2 by5) wfto suggested that a loss of oxygen from an initially

(hypothetically) hyperstoichiometric surface layer might bethe reason for the reduction in D. In the present work thermo-gravimetric analysis, by oxidation to U3O3, indicated an O/Mratio of 2.012 ± 0.006 for specimens annealed in argon at 157O°cin the tungsten furnace, i.e. the specimens gained oxygen underthese furnace conditions as before the pre-anneals the 0/M ratiowas 2.000 ± 0.001 (see Table 1).

* It is probably significant that specimen Tl was repolishedafter pre-annealing in order to remove some surface contamination.No further anneal was given and the specimen was therefore in adeformed state at the start of the diffusion anneal. A furtherpoint is that high diffusion rates within and parallel to thesurface layer are necessary to account for such a large propor-tion of the tracer being able to diffuse down dislocations, ifthe dislocation density is only ̂ 10 6 dislocations/an2. Suchrapid diffusion rates have been observed for thoria(-jl) and more-over they apparently occur over a thick layer U1000A) near thesurface.

- 22 -

Another possibility is that as the diffusion rateshould be dependent on impurity concentration(32)t D couldbe lowered by the solution, or precipitation, of an appro-priate impurity during the initial stages of the anneal.However, one object of pre-annealing the specimens was toavoid this type of effect.

9.2 Comparison with Previous Data

The few previous determinations of thorium (oruranium) diffusion in TI1O2 are shown in Figure 12 and Table4. Measurements of uranium diffusion in UO2 have been sum-marized recently by Belle(1). More recently Reimann andLundy(33) have reported the results of experiments which sug-gest that most of the previously reported UO2 bulk diffusiondata are in error due to the effect of grain boundaries inenhancing the diffusion rates.

9.2.1 Diffusion in Thoria

Considering the thoria work first, the results ofmost interest are the data on single and polycrystal ThC>2obtained by Morgan and Poteat(4) using a-spectrometry andsome sectioning, and the work on polycrystalline ThO2 byHawkins and Alcock(2).

Hawkins and Alcock1s data, although internally consis-tent in terms of temperature variation and apparent linearityof In c vs x2, indicate much higher D values than those ob-tained in the present work (see Figure 12). However, itshould be noted firstly that their range of linearity inIn c vs x 2 was small. The present results provide evidencethat an apparent linearity, observed at intermediate pene-trations, can give a false D value (e.g. specimen T32 Figure6, specimen T4 Figure 7c, see also ref. 18). Secondly Hawkinsand Alcock's diffusion profiles in fact had a steep slope forx & 0.6|jm. The authors suggest that this was due to most ofthe tracer isotopes being "held up" at the surface. It issuggested here that this hold-up was in fact due to the slow-ness of bulk diffusion, the penetration at greater depths

- 23 -

being primarily a result of grain boundary diffusion. Thea-spectrometer used had poor resolution (80 keV, which wouldnot allow the 230-ph a doublet to be resolved). Thus, forexample, for the run they illustrate (their Fig. 1) the low-est measurable diffusion coefficient is about 1.5 x 10~!5 cm2/sec. The present work indicates the true bulk diffusion co-efficient at this temperature (1825°C) to be probably < 1 x10-16 cm2/sec> This would have been undetectable by theirequipment thus explaining the apparent "hold-up" of the bulkof their tracer isotope.

Morgan and Poteat looked at specimens ranging from thevery small grained {^l\m grain size) prepared by the sol gelroute, to single crystals from the Norton Company which wereprobably very similar to those used in the present study. Theyreported that the slopes of the log C vs x 2 plots, decreasedwith distance from the surface, the decrease being more pro-nounced for polycrystals. Also, in general, the diffusioncoefficients increased with a decrease in grain size.

Using ct-spectrometry, Morgan and Poteat got threeestimates of D; (1) from the ratio of the two 2 3 0 ^ peaks at4.68 and 4.62 MeV before and after diffusion, (ii) from anextrapolation of thts profile of the first peak after diffusion,and (iii) from the spectrum of lower energy a particles. Thesethree methods corresponded to penetration ranges of <0.26pm,0.2 to 0.6(jm and 0.4 to 1.2pm respectively. Even in this smallrange the variation in D was as much as two orders of magni-tude for a run at 2300°C.

For polycrystals they used the same techniques togetherwith sectioning, when penetration was sufficient, using weightloss to give the section thickness. Sectioning also gave anear-surface slope much steeper than that at deeper penetra-tions (up to ̂ 10|am) in reasonable agreement with the a-spectro-metry results. The near-surface values approximated to thevalues for single crystals. At deeper penetrations the poly-crystal D values were roughly similar to the values obtainedby Hawkins and Alcock.

Morgan and Poteat concluded that lattice diffusion ismasked by diffusion in grain boundaries and/or subgrain boun-daries.

- 24 -

3 ) , measuring ?-37u diffusion in sintered ThC>2»obtained values for the lattice and grain boundary diffusioncoefficients (using Suzuoka's (24) treatment of grain boundarydiffusion). Sectioning and specimen surface preparation wereby grinding as opposed to polishing. Section thicknesses of~2(jm were determined by weight loss before and after completesectioning and by gauging at ̂ 5pm intervals during sectioning.It is doubtful if the profiles were detailed enough for theresults quoted to be reliable. In all the runs a high tracerconcentration, assumed to be due to a surface bound layer, wasfound in the first section.

If the high concentrations near x = 0 in all theseexperiments are not due to hold-up for reasons other than veryslow lattice diffusion, and if the near-surface material isnot anomalous in some other way (e.g. some type of spacecharge effect(34,35))f the "near-surface" values measuredin the present study and in Morgan and Poteat's experimentsshould be the closest to the lattice diffusion coefficients.The true lattice diffusion values are probably lower stillbecause of the effect of the faster diffusion processes oneven the near-surface slopes. Even a large range (1-2 ordersof magnitude in concentration) of linearity in In c vs x 2 isno guarantee that lattice diffusion is being measured in thissituation. An example of this occurs in reference 36 where alattice diffusion coefficient some 6 times greater than thatobtained by extrapolation from high temperatures, was obtainedin an experiment on polycrystal zinc at ̂ ,0.6 Tm. In the pre-sent work, at ̂ 0.6 Tm, on the very slowly diffusing cationsin ThC>2 and UO2# such an enhancement is even more likely.Other evidence that the near-surface results can be too highis shown in Fig. 12, i.e. Morgan and Poteat's near-surfaceD value for a polycrystal sample at ̂ 2170°C is higher thanthat for a single crystal at 2300°C.

The present results at the lowest temperature are alsoprobably too high because 2/Dt may be comparable to the iso-tope source thickness in this case. If so then, D, obtainedusing the thin film solution to the diffusion equation, wouldbe over-estimated by some 50%.

It is thought therefore that the lattice diffusioncoefficient in this Norton ThO2 is ̂ 5.2 x 10~ 1 5 cm2/sec at2300°C (Morgan and Poteat's data) and ^ 1 x 10~16 cm2/sec at

- 25 -

1846°C (this work).

The effects of stoichiometry and impurities shouldbe considered further. With cation impurity concentrationof perhaps 500 atomic ppm (see Table 1), lattice diffusionin all this work must be extrinsic. On balance the impuri-ties are of valence <4 and may therefore suppress the cationvacancy concentration (32). The activation energy would thenbe the same as in ThO2-x> *n addition runs 1 and 2 were con-ducted under reducing conditions which turned the thoriablack, indicating a removal of oxygen, presumably accompaniedby a reduction in the valence state of some reducible impur-ity. (The reduction was not measurable by oxidation andweight gain measurements, i.e. x, in ThO2-x

w a s <0.Q05.)The effective stoichiometry was thus not the same for eachrun. The Arrhenius plot (Q _ 150 kcals/mole) fitted to thedata is probably not very significant for this reason alone.

The dislocation diffusion measurements shown inFig. 12 point towards low Q and Do values. The diffusioncoefficient due to dislocations i.j ̂ D^ a2 N = D^ 6 LN cm2/secwhere a2 is the dislocation cross-section area, N the numberof dislocations per unit area, and L the distance betweendislocations in the subgrain boundaries. With the subgrainsize» and dislocation contents discussed previously "LN" is-lO 1 - 102 cm"1. Comparing values of Dd 6 in Fig. 12 withthe present "lattice" data or Morgan and Poteat's Arrheniusplot, it can be seen how lattice diffusion will be outweighedby diffusion down dislocations at low temperatures, and quitepossibly at temperatures ^,2000°C U-0.63 Tm) also.

9.2.2 Diffusion in Urania

Comparison of the available results on cation diffu-sion in U02 is complicated by the large deviations fromstoichiometry which easily occur, in addition to the effectsof grain boundaries, dislocations and impurities. Below about1600°C a dry hydrogen atmosphere is needed to prevent oxida-tion while, at higher temperatures, annealing in dry hydrogencauses reduction to UO2-X»

t h e oxygen deficiency produced i n~ „.creasing with temperature. For UO 2 + X, simple theory predicts *

- 26 -

that Dax2 at a given temperature. A similar relation hasbeen observed experimentally(2«5f37). Unfortunately, forcomparison purposes, accurate measurements of small devia-tions from stoichiometry (<0.005) are quite difficult.

Previous results are compared at the température of1575°C, used in the present work, in Table 5. Apart from thestrong dependence of D on stoichiometry, the values for"stoichiometric" specimens range over 3 orders of magnitude.At very small deviations from stoichiometry diffusion willbe impurity controlled. However, it is doubtful whether thefactor of 1000 between the results obtained by Lindner andSchmitz(lOa) and Marin and Michaud(38) fOr sintered specimensis due to this effect alone.

It is proposed here that most experimenters havefailed to detect true bulk diffusion due to the effects ofgrain boundary and dislocation or subgrain boundary diffusion.

The experimental observations which are of particularinterest are (a) the non-Gaussian nature of the complete dif-fusion profiles, found to a greater or lesser extent in everystudy, and (b) the apparent decrease in D with time noted inthis work and by Matzke^5) and Auskern and BPlle(39). Marinand Michaud(38) did not specifically mention this time depen-dence but it is significant that the lowest D value determinedwus their value for a polycrystal specimen after a 1 monthanneal ( cf~ times £ 1 day in other studies).

Opposing evidence which needs to be explained is theapparent success of Yajima et al(40), Hawkins and Alcock <2)and Alcock et al(41) i n separating grain boundary from bulkdiffusion. In the latter work(2»4!) bulk diffusion valuesobtained from polycrystals were always in good agreement withvalues obtained from single crystals in which the profile nearthe surface was ignored as being due to a surface bound layer.The explanation proposed here is that these "bulk" diffusionvalues were enhanced by dislocation diffusion. If the profileshad been examined in more detail an apparent diffusion coef-ficient would have been obtained from the slope at x - 0 whichwould be more nearly representative of true bulk diffusion.

- 27 -

This approach was used in the present work and also essen-tially by Reimann and Lundy (Lundy(42)) a n d i s i m p l i c i t i n

Marin and Michaud's result.

The present values for DTh in UO 2.QI (see Table 3)are similar to those of Marin and Contamin (37) for Du inhypers toichiome trie U0 2 (Table 5). The only other datawhich are compatible with these results, are the very low Dvalues, for "stoichiometric" uo2, obtained by Reimann andLundy(33), a n d b y Matzke(5) for long annealing times. Reimannand Lundy1s experiments show how grain boundaries (in verylarge grained crystals as opposed to the usual sinteredspecimens) can increase the amount of diffusion to greaterdistances and also lower the slope of In c vs x 2 near x = 0.A feature of their results (Lundy(42)) which illustrates theunreliability of results obtained even when short circuitingeffects are recognized, is that an apparent D value of ̂ 2.5 x10-15 cm2/sec obtained from the near-surface slope of a largegrained polycrystal (at 1880°C, Figure 2 in ref. 33) is somethree times lower than the value quoted for a single crystal.At the high temperatures they employed (1600-2000°c) theirhydrogen anneals probably produced appreciable substoichio-metry (which would increase with temperature, making the Do

and Q values invalid). A difference in stoichiometry mightbe the reason for the difference between the values.

These low D values for "stoichiometric" UO2 are com-parable with the present results for DTh i° thoria, e.g.at 1700°C Marin and Michaud obtained DyUn UO2.00) = 5 x10~16 cm /sec and Reimann and Lundy obtained 10 x 10~16 cm2/sec.

Taking the melting points of U02 and ThO2 as 3153°Kand 3540°K(8), the comparable temperature relative to theM.P. for thoria is 1943°C, at which temperature the presentdata indicate D T ^ (in ThO2) =" 8 x 10-16 cm

2/sec (see Figure 12)*.

* It is interesting that for CaF2 (Tm = 1 7 7 5 ° K ( 8 ) ) the com-parable temperature is 838°C, at which temperature Matzke's(43)self diffusion data indicates a Ca diffusion coefficient of16 x 10~ 1 6 cm2/sec.

- 28 -

10. SUMMARY

A precision sectioning technique has been developedand applied to diffusion studies of 228Th in ThO2 and U02»the diffusion profiles obtained have been verified by thea-spectrum degradation technique. Diffusion experimentswere performed on single crystals. In ThO2 the measurementswere made in the range 1850 to 2000°C while in U02 a seriesof anneals was made at one temperature, 1575°C.

Non-Gaussian profiles were observed in every case.These are thought to result from a combination of latticediffusion and short circuit diffusion via dislocations andsubgrain boundaries. It is not thought that any appreciablesurface hold-up effect exists, but rather that the truecation lattice diffusion coefficients at these temperatures(~0.6 Tm) are very small. (Experiments at higher tempera-tures are hindered by evaporation and the associated surfacedeformation of the specimens.) Upper limits for the latticediffusion coefficients are obtained from the limiting slopesof the log c vs x^ profiles as x -• 0.

Estimates of the "dislocation" contribution to dif-fusion have been made for the thoria specimens using asimple Fisher type analysis of the profiles at deeper pene-trations. It appears that the faster diffusion processmay well mask lattice diffusion at the temperatures used inthis work.

The measurements on U02 showed an apparent decreasein D with annealing time. The limiting values after longannealing times are considered to be the correct ones.

Previous work has been considered in the light ofthe present results. It is concluded that most latticediffusion values, obtained from studies of either singlecrystals, or polycrystals, even after correcting for grainboundary diffusion(2«3,41)f a r e too high due to the effectsof short circuiting diffusion.

Data which are considered to be most representativeof volume diffusion are the present results on ThO2 andu°2.01» and the low diffusion rates reported for UO2 byReimann and Lundy(33)f Marin and Michaud(38) anrj Matzke (

5)(see Table 5).

- 29 -

ACKNOWLEDGEMENTS

The experimental assistance provided by A. Hunton andJ. Moerman, and much helpful advice from B. G. Childs, who in i -tiated this work, i s very gratefully acknowledged. The authoralso wishes to thank G.V. Kidson for useful discussions andfor suggesting the method of mounting the specimens for sec-tioning, G.M. Hood for advice and i.H. Crocker for providingthe Spark Source Mass Spectrometric analyses. Thanks are alsodue to T. Bruce for help with the analyses for uranium.

- 30 -

REFERENCES

(1) J. B e l l e , J. Nucl. Mat. .30 (1969) 3 .

(2) R. J. Hawkins and C.B. Alcock, J. Nucl. Mat. 26 (1968) 112.

:..3) M. Furuya, J. Nucl. Mat. 26. (1968) 123.

(4) C.S. .organ and C E . Poteat, ORNL Metals and Ceramics Div.Annual Progress Report for period ending June 30, 1968;also private communication.

(5) Hj. Matzke, J. Nucl. Mat. 3£ (1969) 26.

(6) L. DeJonghe, W. Van Lierde and R. Geuens, J. Sci. Instrum.43_ (1966) 325.

(7) G.W. Leddicotte and M.A. Mahlman, Paper No. A/Conf. 8/P/117,p.250, International Conf. Peaceful Uses of Atomic Energy,Geneva, August 1955.

(8) Thermophysical Properties of High Temperature Solid Materials,Vol. 4, Part I, Ed. Y.S. Touloukian, (MacMillan 1967).

(9) K.L. Cheng, Analytical Chem. 30 (1958) 1027.

(10a) R. Lindner and F. Schmitz, Z. Naturforsch. 16. (1961) 1373.

(10b) F. Schmits and R. Lindner, J. Nucl. Mat. J/7 (1965) 259.

(11) U. Fano, Ann. Rev. Nucl. Sci. L3 (1963) 14.

(12) Nat. Bur. Standards Handbook, No. 79, "Stopping Powers forUse With Cavity Chambers", (1961).

(13) A. Chetham-Strode, J.P.. Tarrant and R. J. Silva, I.R.E. Trans.Nucl. Sci. N S ^ , No. 1 (1961) 59.

(14) P.O. Perron, AECL Report, AECL-3072 (1968).

(15) T.L. Markin, V. J. VJheeler and R. J. Bones, J. Inorg. Nucl.Chem. .30 (1968) 807.

- 31 -

(16) G.M. Hood, Phil. Mag. 2JL (1970) 305.

(17) L. G. Harrison, Trans. Faraday Soc. 5T_ (1961) 1191.

(18) T.S. Lundy and R.E. Pawel, Trans. Met. Soc. AIME 245(1969) 283.

(19) E.W. Hart, Acta Met. 5. (1957) 597.

(20) B. JV Wuensch and T. Vasilos, J. Amer. Ceram. Soc. 47_ (1964)63; J. Amer. Ceram. Soc. 49. (1966) 433).

(21) J.C. Fisher, J. Appl. Phys. 22_ (1951) 74.

(22) R.T.P. Whipple, Phil. Mag. 45 (1954) 1225.

(23) A.D. LeClaire, Brit. J. Appl. Phys. 14 (1963) 351.

(24) T. Suzuoka, Trans. Jap. Inst. Metals £ (1961) 25.

(25) R, Smoluchowski, Phys. Rev. §2 (1952) 482.

(26) P.V. Pavlov, V.A. Panteleev and A.V. Maiorov, Sov. Phys.Solid State 6_ (1964) 305.

(27) L.C. Luther, J. Chem. Phys. 43. (1965) 2213.

(28) A.T. Chapman, G. W. Clark, D.E. Hendrix, C.S. Yust andO.B. Cavin, J. Amer. Ceram Soc. j>3_ (1970) 46.

(29) D.K. Dawson and L.W. Barr, Proc. Brit. Ceram. Soc., No. 9,(1967) 171; Barr and Dawson AERE-R6234.

(30) R.N. Ghostagore, Phys. Rev. 155 (1967) 603.

(31) R.M. Berman, AEC Research and Development Report WAPD-TM-843(1969).

(32) A.B. Lidiard, J. Nucl. Mat. 19 (1966) 106.

(33) D.K. Reimann and T.S. Lundy, J. Amer. Ceram. Soc. 52. (1969)511.

- 32 -

(34) K. Lehovec, J. Chem. Phys. 2JL (1953) 1123.

(35) I.M. Li fshi t s and Ya. E. Geguzin, Sov. Phys. Solid State2 (1965) 44.

(36) E. Wajda, Acta Met. 2 (1954) 184.

(37) J. F. Marin and P. Contamin, J. Nucl Mat. J30 (1969) 16.

(38) J.F. Marin and H. Michaud, Compt. Rend. Acad. Sci. (Paris)261 (1965) 693.

(39) A.B. Auskern and J. Belle, J. Nucl. Mat. 2 (1961) 267.

(40) S. Jajima, H. Furuya and. T. Hiroi, J. Nucl. Mat. 26_ (1968)112.

(41) G. B. Alcock, R. J. Hawkins, A.W.D. Hills and P. McNamara,Paper SM-66/36, IAEA Symp. Thermodynamics (Vienna, 1965).

(42) T.S. Lundy (ORNL), private communication (1969).

(43) Hj Matzke and R. Lindner, Z. Naturforsch. 19a (1964) 1178.

(44) P. Nagels, W. Van Vlierde, R. DeBatist, M. Denayer, L. DeJongheand R. Gevers, Paper SM-66/46, IAEA Symp. Thermodynamics(Vienna, 1965).

(45) J. F. Marin, H. Michaud and P. Contamin, Compt. Rend. Acad.Sci. (Paris) Ser. C, 264 (1967) 1633.

TABLE 1

CHEMICAL ANALYSES

Spark Source Mass Spectrometry

Thoria Urania *

Principal cationimpurities

Range of ImpurityConcentrationsfound ppm Thorium

atoms

Principal cationimpurities

ImpurityConcentrations

(One Analysis)

LiBeNaAlSiCaFeYZr

Principal snionimpurities

CNSCl

In addition:

B, F, Mg, P. K, ScZn, Ga, Ge, As, SeBa, the naturally

0 -0 -

30 -300

10 -1 -2 -

100 -10 -

300 -20 -2 -4 -

, Ti, Cr, Mn,, Br, Kr, Rg

100100100

10010003003000100

io4100010030

Co, Ni, CU,Sr, Kb, Rh,

occurring rare earths,and U; have been detected at concentrationsof-v 0.1 to- 10 ppm-

KCaFeNiZrTh

Anions

CNSCl

F, Na, Mg, AlV, Cr, Mn, RGwere detectedor ~ 0.1 t o -

> 100 ppm ea.

> 100 ppm ea.

, Si, P, Sc. Ti,, Y, Ba, La.at concentrations30 ppm.

The figures obtained in these complete Mass Spectrometric analysesare only semi-quantitative (this is partly reflected in the widevariations between samples). Several ThO2 samples were also analysedspectrographically. These usually indicated somewhat lower con-centrations for the impurities. Al, Fe and Si were the principalimpurities, with concentrations generally of the order of 30 ppmatoms of thorium. Most other elements went undetected.

* O/y ratio; 1.976 ± 0.005 as received, 2.000 ± 0.001 after (wet)hydrogen heat treatment (see section 3).

TABLE 2

VOLUME AND SHORT CIRCUIT DIFFUSION COEFFICIENTS228_

FOR Th DIFFUSION IN ThOn

S p e c .

Tl

T2

T31T32

T4

Temp.°C

2045T

1995

1846II

1924

10T°K

4.31

4.41

4.72II

4.55

Annealing Time(hours)

14

50

20II

17

D/ sec

4 x 10-15

1.9x10"1 5

< 2 x 10"16

4.9 x 10- 1 6

Dd6

Cm̂ / sec

2.4 x l 0 " 1 7 *

9.7 x l 0 " 1 8

1.1x10~17 *5 .4x10" 1 8

2.6 x 10~17

t Includes 50SC estimated temperature correction (see page 12)* Most accurate dislocation diffusion measurements (These

specimens showed an extensive region of linearity in lnc vs x)

TABLE 3

APPARENT VOLUME DIFFUSION COEFFICIENTS228.

FOR Th DIFFUSION IN UO,2.01

1st run 1570°C spec U2

Annealingtime (h)

4

21

35

Dcm / sec

~3 x 10~14

2.3 x10" 1 4

1.2 x i o " 1 4

l.Oxlo"14

2nd run 1574°C spec U2

Annealingtime (h)

14

32

Dcm / sec

2 .5x10" 1 5

1.5x10" 1 5

3rd run 1575°C spec U3

Annealingtime (h)

20

39

59

102

2cm /sec

3.3 x i o " 1 5

3.4x10~15

2.2x 10"15

1.9x10"15

TABLE 4

PREVIOUS MEASUREMENTS OF CATION DIFFUSION IN THORIA

Reference

Morgan and Poteat,1969, ref. 4

Hawkins andAlcock, 1968,ref. 2

Fuxuya, 1968, ref.3 (uranium diffu-sion)

Matzke, 1969. ref.5

Specimen Material

Norton Arc Fusedsingle crystals +polycryatal speci-menta grain sizedown to _1 um

Sintered polycrystalsgrain size .,100 \sa

Sintered pellets

Single crystals andsintered specimens

Techniaue

a-spectrametrywith variationssectioning forsome polycrystals

a-spectrometry

Sectioning bygrinding

a-apectrome try228-fh isotope

Annealinq Atmosphere

Argon for T > 1800°coxidizing atmosphere atlower temperatures

Air, C0/O>2 mixtures,hydrogen, vacuum.Oxygen partial pres-sure 10-0-7 t o 10-î0atmos.

Argon,reducing furnacecomponents

TemperatureRanqe

1300°Cto

2300°C

1600=Cto

2100-C

1800°Cto

2000"C

1500°C

Results

Single crystal results at sl800°Cfor penetration range <0.6 \m aregood fit to D=2xl0-7 exp-7400Q/R1cm2/sec. For polycrystal alldata «2170-c are fitted by:

D=4.1xlO"9 exp-68100/RT cm2/sec near the surface)

D=2.6x10-7 exp-69000/RT cm2/sec for x from 0.2 to 0.6 \m;

D-7xlO-6 exp-65200/RT cmVsecat deeper penetrations.

D=1.25xl0-7 exp-58B00/RT cm2/sec

D=1.1x10-4 exp-76400/RT cm2/sec lattice diffusion

Djj-2.35x10-9 exp-47900/RTcm^/sec grain boundarydiffusion

D=3.5x10-16 cm2/sec inde-pendent of tine

* Extrapolated using authors data.TABLE 5 t Extrapolated using Q - 90 k calB.

PREVIOUSLY PUBLISHED DATA OH URANIUM DIFFUSION 191 UOj COMPARED WITH PRESENT DATA OH THORIUM DIFFUSION IN UO, AT ~1575°C

Reference

Present work.Thorium diffusion.

Yajima e t al 1966Réf. 40

Lindner and Schmitx1961. Ref. loa)

Auskern and Belle1961. Ref. 39

Nage13 e t al 1966Ref. 44

Hawkins and Alcock1968. Ref. 2

Alcock Qt a l 1966Ref. 41

Hatzke 1969 Ref. 5

Reixiann & Lundy1969 Ref. 33

Marin & Contamin1969 Ref. 37

Marin & MichaudRef. 38

Specimen type

Single crystals

Sintered specs.

Sintered specs.

Sintered specs.

Single crystals

Sintered specs.+ single crystals

Sintered specs.& single crystals

Single c iys ta l s £large grained cryst

Sintered specs.

• •

Annealing con-di t ions . Stoichion

Argon0/0 = 2.01

Sealed under A inTa capaule 0/u.?

Hydrogen

Hydrogen

Vacuum O/U=?

Co/Co, f ixtures

0/0=2.10/U=2.01

HydrogenBtoichioraetr ic

Hydrogen

Hydrogenals

Argon/oxygenmixture0/U = ~2.110/0 =-2.0450/0 - -2.005

Pure Argon, re-ducing environment0 / 0 i 2.002

Method

a-spectrometry+ sectioning

Sectioning

a-spectrometry

Surface activit;decrease. Somesectioning.

Precisionsectioning.

a-snectrometry

a-spectrometry

a-spectr ome try

a-spectrometry

N

Diffusion Coefficientcmz/sec at 1575°C

< 1.5-1.9 x i o " 1 5

1.63 x 10"13 *

1.15 x l o " 1 3

1.92 x io" 1 *

- 1 . 9 x l o " 1 4

~ 4 . 5 x l O ~ "~ 7 x 10

2.5 x i o " 1 5

< 5 x 10"16 t

~10~13for s intersafter —5 hr anneal

1.8 x 10"1 0

~3 x 10~2 x 10"15*~1 xtlO"16t

Comments

Log C vs x non l inear. D time dependent.

g.b. and la t t i ce diffusion coeffs . obtained.Sectioning technique crude, insuff. pointsnear surface

Apparent D increased with x. Took slope atdeeper penetration.

Decrease of D (by surface act iv . dec.) withtime, and the sectioning results , evidence ofg.b. diffusion

Some evidence of lower near surface D in onlypub. profi le , given in ref. 6

For s inters l a t t i c e diffusion coeffs . , separatedfrom g.b. diffsn, agree with single crystalvalues.

Slopes of log C vs x taken in restricted range,x ~ 0 . 7 to ~2 urn, concentration variation lessthan one order of magnitude.

Rate of di f fsn. after >1DO hra. at 1500°C and1S5O°C not measurable. Faster diffusion alwaysoccurred i n i t i a l l y . Sinters always gave higherD's than single crys ta l s .

Grain boundary e f f ec t s on diffusion profileclearly shown

Log C vs x often curved (37). In ref. 45 theseauthors got same 0 value for single & poly-crystals of UOj.Qg. Value here for "stoichiomet-r i c U0- iB estimated from value 5 x 10"16 cm2/sec from a 3 month anneal at 1700°C (38).

i l e t ->.( ;, fi

Figure 1 The automatic polishing machine.

1000

CHANNEL NUMBER N

Figure 2 y counts from a 0.056nm thick ThO2 section.A) Prom 212pb daughter of the 228iph tracer.B) After neutron activation (212Pb counts

in A) substracted).

5.5

a ENERGY (MeV)

6.0

1600 —

1400 —

1200 —

1000 —

800 —

600

400 —

200 <—

50 200CHANNEL NUMBER

Figure 3 228<j<h a spectra (excluding the highenergy 212po peak) before and afterdiffusion (Specimen U3 diffused 20hrs at 1575°C) obtained using aSurface Barrier Detector.

250

0.1 0 . 2 0 . 3 0 . 4 0 .5 0 . 6—i

X (MICRONS)

0.7

D = 1.9 X I 0 - ' 5 c m V s e c

0 = 4 . 0 X 1 0 - ' 5 c m V s e c

I I 1 I

0.8—r~

0.9

I J_

O.t 0 . 2 0 . 3 0 . 4 O.S 0 . 6 0 .7 0 . 8 0 . 9

X2 (MICRONS)2

Figure 4 Th in ThO2# Log c vs x2.

Run 1 14 hrs at 2045°C*.Run 2 50 hrs at 1995°C.

* Includes temperature correction, see page 12.

m a

T h O j S E C T I O N I N G L O G C VS X

o

b

I oI O ,

E«tf>IPOLA!ION OF NE«R SURFACE REGION

HUN » S

e o

II 12 13 »

• (MICRONS)

Figure 5 Th in ThO2, Log c vs x, Runs I and 2. Dashed curvesnear x = 0 show region of linearity in log c vs x^.

e •

I . I , , I

31V3S 301

Ab»aiiaa*)

A)

0 01 02 03 04 05 .06 .07

: 4.9 I 10- '6 cm'.'sec

I I I \ i I I n i I

O SECTIONING U»TA

• a - SPECTROMETRY DATA (LOVER POINTS CORRECTEDFOR a-PEAK TAIL)

j I L j L

o

0 = 2 0 X 10" ! cm- sec

I I

fUSTHEl! POINTS

1 10 I 0.2 0.3 0.4 O S 0 6 0 5 10

X1 (MICRONS)120 25 30 35

Figure 7 Th in ThC>2. Run 4 17 hr at 1924°C. (All plots log cvs x^ in microns2. )

K- UJ .

too

=p—r

\\i a

" \

—

-

—

i i

ii

1 1 | 1 1 1

SPEC T32

o

SPEC T31

1 1 1 1 1 1

1 I 1 1 1

O SECTIONING DATA

s. o

1 1 1 1 1 1

1 !

—

-

1 ! 110

X (MICRONS)

15

Figure 8 Th i n ThC>2» Run 3. Log c vs x.

"i i i i i r

O SECTIONING

• a - SPECTROMETRY

SPEC U!

\

\

J I I I L

i 1 1 r

O 2 I 10" " cm' stc

0 O S 1 0 I S 20 25 3 0 * 0

X' (UICBONS)'

10 IS 20 25 30

Figure 9 Th in UO2, Run 1 Log c vs x2 35 hr at 1570°C.

O SECTIONING POINTS

a - SPECTROMETRY CURVES

(POINTS AT 0.013/i.m INTERVALS)

• a - SPEC. POINTS AT X = O

2 .0

X2 (MICRONS)2

3.0

Figure 10 Th in U02, Run 2 Log c vs x2 32 hr at 1574°C.

Near Surface Slope—»• Decreasing Slope

ITR

AR

YAR

BIO

NJT

RA

TIC

Eh

o

J SPEC U 2

( j ) 20 HOUR ANNEAL

Q) 39 HOUR ANNEAL

(3 ) 102 HOUR ANNEAL

a - SPECTROMETRY DATAPOINTS AT 0.024/xm INTERVALS

0.2 1.00.4 O.fe 0.8

X2 (MICRONS)2

Figure 11 Th in UO2, Run 3 Log c vs x 2 1575°C.

_ "Near Surface" Slopes

1.2

8 S

T-C

2300 2200 2100 2000 1900 1800

-1110

io-12

io-13

10-14

10,-15

i-tB10

io-'

1O-18

T TKEY TO MORGAN AND POTEAT DATA POINTS

A • • SINGLE CRYSTAL

A O Q POLY CRYSTALX <. 26 0 .2 - 0. fa 0 .4 - 1.2/rni

FURUYA (U diff.)

HAWKINS & ALCOCK

MORGAN & POTEAT

3.8

PRESENT WORKD VALUES FROMNEAR SURFACE SLOPES

* \

PRESENT WO'RKSHORT CIRCUIT DIFFUSION OVALUES OF Dd S FROM FISHER ANALYSIS

I I I4.0 4.2 fl.4

YTjjMX 10*)

4.t> 4.8 5.0

Figure 12 Thoria diffusion data. Arrhenius plots shown forthe present work are D (Volume) =0.35 exp -149,500/RT cm2/sec and D^ô = 8x10-14 - 37,300/RTcm3/sec (based on the two most accurate analysesfor specimen Tl and T31). Do and Q values for theother plots are given in Table 4. (Morgan andPoteat's plot is a best fit to their single crystalnear-surface data in the range 1300 to~1800°C).

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